Problem $3$: A $3-$phase induction motor with $10$ poles is connected to a voltage source with $v_s(t)=210cos(250t)V_{rms}.$ The motor has $R_s=4,R_r^{\text{'}}=2,x_s=15,x_r^{\text{'}}=1,$ and $x_m=50$

a$)$ Sketch the speed torque curve for this motor. The curve only needs to be approximate, however, you should give the value on the curve for the starting torque, maximum torque, speed at maximum torque in rpm$,$ and maximum speed of the motor in rpm and in rad$/$sec$.(15$ points$)$

b$)$ What are all of the possible motor speeds in rpm and slips if the developed torque, $T_{\text{d}\text{e}\text{v}},$ is $8$ Nm $?(10$ points$)$